The major purpose of this research is to develop robust and efficient methods for the analysis and design of complex data that are encountered in cancer clinical trials. The research will focus on four broad topics. 1. We will develop a comprehensive theory that uses auxiliary baseline auxiliary covariates that are correlated with the primary response variable to develop estimators and tests of treatment difference in randomized clinical trials that are more efficient than current methods. 2. We will extend the methodology from Aim 1. to consider cases where the primary outcome is missing on a subgroup of patients because of loss to follow-up. 3. Semi parametric locally-efficient estimators for the regression parameters in a proportional hazards model that models the relationship of survival and longitudinal data through common subject-specific random effects using a joint model will be developed that are robust to misspecification of the distribution of the random effects. This methodology will also be applicable to finding estimators for the regression parameters in a proportional hazards model with covariates that are measured with error. 4. Two-stage and multi-stage randomized clinical trials is an efficient way of conducting studies with the primary purpose of comparing different time-dependent (adaptive) treatment policies. We will develop weighted log rank tests that can validly be used to test for differences in treatment policies with such designs using censored survival data. Relevance: Because of limited resources, either money or patients, it is imperative that we take advantage of state of the art designs and analyses to get the most efficient use of the data that are collected in a clinical trial so that we have the best chance of answering the scientifically relevant questions. At the same time we want the methods to be as broadly applicable as possible without having to make unnecessary assumptions. The methods that will be developed will use cutting edge theory to accomplish these goals.